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math 411 homework2
Course: MATH 411, Fall 2011School: Texas A&M
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A&M Texas University Department of Mathematics Volodymyr Nekrashevych Fall 2011 Math 411 -- Problem Set 2 Issued: 09.09 Due: 09.16 2.1. A bet is said to carry 3 to 1 odds if you win $3 for each $1 you bet. What must the probability of winning be for this to be a fair bet? 2.2. Five people play a game of "odd man out" to determine who will pay for the pizza they ordered. Each flips a...
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A&M Texas University Department of Mathematics Volodymyr Nekrashevych
Fall 2011
Math 411 -- Problem Set 2 Issued: 09.09 Due: 09.16
2.1. A bet is said to carry 3 to 1 odds if you win $3 for each $1 you bet. What must the probability of winning be for this to be a fair bet? 2.2. Five people play a game of "odd man out" to determine who will pay for the pizza they ordered. Each flips a coin. If only one person gets heads (or tails) while the other four get tails (or heads) then he is the odd man and has to pay. Otherwise they flip again. What is the expected number of tosses needed to determine who will 2.3. pay? A man and his wife decide that they will keep having children until they have one of each sex. Ignoring the possibility of twins and supposing that each trial is independent and results in a boy or a girl with probability 1/2, what is the expected value of the number of children they will have? 2.4. Suppose we pick a month at random from a non-leap year calendar and let X be the number of days in the month. Find the mean and variance of X. 2.5. Can we have a random variable with EX = 3 and EX 2 = 8? 2.6. In a class of 19 students, 7 will get A's. In how many ways can this set of students be chosen?
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Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 3 Issued: 09.16 Due: 09.233.1. A tourist wants to visit six of America's ten largest cities. In how many ways can she do this if the order of her visit
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 4 Issued: 09.23 Due: training4.1. If we flip a coin 5 times, what is the probability that the number of heads is an even number? 4.2. Three students ea
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 5 Issued: 10.08 Due: 10.145.1. Two events have P (A) = 1/4, P (B|A) = 1/2, and P (A|B) = 1/3. Compute P (A B), P (B), and P (A B). 5.2. A friend flips
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 6 Issued: 10.17 Due: 10.246.1. A group of 20 people go out to dinner. 10 go to an Italian restaurant, 6 to a Japanese, and 4 to a French restaurant. Th
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 7 Issued: 10.24 Due: training7.1. Suppose 60% of the people subscribe to newspaper A, 40% to newspaper B, and 30% to both. If we pick a person at rando
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 8 Issued: 11.01 Due: 11.098.1. Suppose X has density function f (x) for a x b and Y = cX + d, where c > 0. Find the density function of Y . 8.2. Suppos
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 9 Issued: 11.15 Due: 11.239.1. 20 people get on an elevator on the first floor of a seven-story building. Each gets off at one of the six higher floors
Texas A&M - MATH - 411
Texas A&M University Department of Mathematics Volodymyr NekrashevychFall 2011Math 411 - Problem Set 10 Issued: 11.29 Due: training10.1. Show that if X is exponential(1), then Y = X/ is exponential(). 10.2. Suppose that X and Y have joint density f (x,
Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
MATH 151, FALL SEMESTER 2011 COMMON EXAMINATION I - VERSION B Name (print): Signature: Instructor's name: Section No: Part 1 Multiple Choice (12 questions, 4 points each, No Calculators) Write your name, section number, and version letter (B) of the exam
Texas A&M - MATH - 151
MATH 151, FALL SEMESTER 2011 COMMON EXAMINATION I - VERSION B - SOLUTIONS Name (print): Signature: Instructor's name: Section No: Part 1 Multiple Choice (12 questions, 4 points each, No Calculators) Write your name, section number, and version letter (B)
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Texas A&M - MATH - 151
MATH 151, FALL 2011 COMMON EXAM II - VERSION A Last Name: Signature: KEY First Name: Section No:PART I: Multiple Choice (15 questions, 4 points each. No Calculators) Write your name, section number, and version letter (A) of the exam on the ScanTron form
Texas A&M - MATH - 151
MATH 151, FALL 2011 COMMON EXAM II - VERSION B Last Name: Signature: First Name: Section No:PART I: Multiple Choice (15 questions, 4 points each. No Calculators) Write your name, section number, and version letter (B) of the exam on the ScanTron form.1.
Texas A&M - MATH - 151
MATH 151, FALL 2011 COMMON EXAM II - VERSION B Last Name: Signature: KEY First Name: Section No:PART I: Multiple Choice (15 questions, 4 points each. No Calculators) Write your name, section number, and version letter (B) of the exam on the ScanTron form
Texas A&M - MATH - 151
MATH 151, FALL SEMESTER 2011 COMMON EXAMINATION 3 - VERSION A Name (print): Signature: Instructor's name: Section No: Part 1 Multiple Choice (13 questions, 4 points each, No Calculators) Write your name, section number, and version letter (A) of the exam
Texas A&M - MATH - 151
MATH 151, FALL SEMESTER 2011 COMMON EXAMINATION 3 - VERSION A - SOLUTIONS Name (print): Signature: Instructor's name: Section No: Part 1 Multiple Choice (13 questions, 4 points each, No Calculators) Write your name, section number, and version letter (A)
Texas A&M - MATH - 151
MATH 151, FALL SEMESTER 2011 COMMON EXAMINATION 3 - VERSION B Name (print): Signature: Instructor's name: Section No: Part 1 Multiple Choice (13 questions, 4 points each, No Calculators) Write your name, section number, and version letter (B) of the exam
Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
Spring 2011 Math 151Exam I Version B Solutions9. E The angle between the gravity force (weight) and the motion of the block is 60 , so the work done is W = |F|D| cos 60 = 1 = 300 ft-lbs. (30)(20) 2 10. B f (3) = lim f (3 + h) - f (3) = lim h2 - 4h + 7 =
Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
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Texas A&M - MATH - 151
MATH 151, SPRING 2011 COMMON EXAM III - VERSION A LAST NAME, First name (print): INSTRUCTOR: SECTION NUMBER: UIN: SEAT NUMBER: DIRECTIONS: 1. The use of a calculator, laptop, or computer is prohibited. 2. In Part 1 (Problems 1-12), mark the correct choice
Texas A&M - MATH - 151
Spring 2011 Math 151Exam III Version A Solutions1. D Since the numerator and denominator both approach 0, use L'Hospital's Rule: ex - cos x - 2x ex + sin x - 2 1 lim = lim = . 10. E An antiderivative of f (x) = ln x means 2 - 2x x0 x0 x 2x - 2 2 its der
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Texas A&M - MATH - 151
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